Desargues graph - Revision history

Vipul at 22:18, 29 May 2012

2012-05-29T22:18:03Z

← Older revision		Revision as of 22:18, 29 May 2012
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	\| {{arithmetic function value\|size of vertex set\|20}} \|\| As Levi graph of Desargues configuration: number of points + number of lines in the configuration = <math>10 + 10 = 20</math><br>As bipartite Kneser graph with parameters <math>n = 5, k = 2</math>: <math>2 \binom{n}{k} = 2 \binom{5}{2} = 2(10) = 20</math><br>As generalized Petersen graph <math>G(n,k), n = 10, k = 3</math>: <math>2(10) = 20</math>		\| {{arithmetic function value\|size of vertex set\|20}} \|\| As Levi graph of Desargues configuration: number of points + number of lines in the configuration = <math>10 + 10 = 20</math><br>As bipartite Kneser graph with parameters <math>n = 5, k = 2</math>: <math>2 \binom{n}{k} = 2 \binom{5}{2} = 2(10) = 20</math><br>As generalized Petersen graph <math>G(n,k), n = 10, k = 3</math>: <math>2(10) = 20</math>
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			\| {{arithmetic function value\|size of edge set\|30}} \|\| As Levi graph of Desargues configuration: number of incidences between points and lines = (number of lines) * (number of points on each line) = <math>(10)(3) = 30</math><br>As bipartite Kneser graph with parameters <math>n = 5, k = 2</math>: <math>\binom{n}{k,k,n-2k} =\frac{n!}{k!k! (n - 2k)!} = \binom{5}{2,2,1} = 30</math><br>As generalized Petersen graph <math>G(n,k), n = 10, k = 3</math>: <math>3n = 3(10) = 30</math>
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Vipul at 22:14, 29 May 2012

2012-05-29T22:14:25Z

← Older revision		Revision as of 22:14, 29 May 2012
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	# It is the [[defining ingredient::bipartite Kneser graph]] with parameters 5,2		# It is the [[defining ingredient::bipartite Kneser graph]] with parameters 5,2
	# It is the [[defining ingredient::generalized Petersen graph]] <math>G(10,3)</math>.		# It is the [[defining ingredient::generalized Petersen graph]] <math>G(10,3)</math>.

			==Arithmetic functions==

			===Size measures===

			{\| class="sortable" border="1"
			! Function !! Value !! Explanation
			\|-
			\| {{arithmetic function value\|size of vertex set\|20}} \|\| As Levi graph of Desargues configuration: number of points + number of lines in the configuration = <math>10 + 10 = 20</math><br>As bipartite Kneser graph with parameters <math>n = 5, k = 2</math>: <math>2 \binom{n}{k} = 2 \binom{5}{2} = 2(10) = 20</math><br>As generalized Petersen graph <math>G(n,k), n = 10, k = 3</math>: <math>2(10) = 20</math>
			\|}

Vipul: Created page with "{{particular undirected graph}} ==Definition== The '''Desargues graph''' is a particular graph on 20 vertices defined in the following equivalent ways: # It is the [[defini..."

2012-05-29T22:03:27Z

Created page with "{{particular undirected graph}} ==Definition== The '''Desargues graph''' is a particular graph on 20 vertices defined in the following equivalent ways: # It is the [[defini..."

New page

{{particular undirected graph}}

==Definition==

The '''Desargues graph''' is a particular graph on 20 vertices defined in the following equivalent ways:

# It is the [[defining ingredient::Levi graph]] of the [[defining ingredient::Desargues configuration]]
# It is the [[defining ingredient::bipartite Kneser graph]] with parameters 5,2
# It is the [[defining ingredient::generalized Petersen graph]] <math>G(10,3)</math>.